Vajpayee, however, rejected opposition claims the United States had put direct pressure on the two estranged neighbours to sort out their five decades of hostilities.
The premier told the Times of India newspaper that a "circumstantial factor" was linked to his gesture in Kashmir on April 18 last year when he extended a "hand of friendship" to Pakistan to kick off a fresh peace initiative.
"The war in Iraq was a warning to all developing countries (that) we needed to resolve our disputes peacefully and speedily amongst ourselves," the 79-year-old Vajpayee told the English-language daily.
"The number of people in Pakistan who think likewise is steadily growing," Vajpayee said, without naming individuals who back the ongoing peace process between the two South Asian countries.
India and Pakistan, who have fought two of their three wars over Kashmir since independence in 1947, came dangerously close to a fourth war in 2002 following an attack on the Indian parliament by gunmen New Delhi said were sponsored by Pakistan.
The 10-month standoff, during which a total of 700,000 troops massed on their borders, ended following a series of visits to the two countries by Western leaders, fearful that spiralling tensions could trigger a nuclear holocaust in South Asia.
Vajpayee told the paper he was convinced Islamabad would not try to derail the ongoing peace process, which has led, inter alia, to the first full tour of Pakistan by an Indian cricket team in almost 15 years.
"I have faith in humanity of people everywhere, including the people of Pakistan," the poet-cum premier commented.
"There is realisation that fighting more wars is neither a solution nor an option," Vajpayee said, insisting the initiative was the result of a bilateral consensus rather than international pressure.
"People feel that talks have begun after pressure from the US," he said of a dialogue started in February which aims to resolve a raft of regional disputes.
"At the time (April 18) there was no pressure. Of course, whenever they (US) met us, they said we should talk. This time there was no pressure. They did not even know that some talks had begun," Vajpayee said.
The prime minister, however, said the mammoth deployment of troops to Pakistan's borders was meant to send a strong signal.
"No, it was needed. Very much so. It was necessary to convey that we would not tolerate things silently as we had in the past," he said.
India accuses Pakistan of arming and training Islamic insurgents in the Indian zone of Kashmir. Islamabad denies the allegation but says it offers moral and diplomatic support to what it argues is the Kashmiris' just struggle for self-determination.
The anti-Indian rebellion in the disputed Himalayan territory has claimed more than 40,000 lives since the start of the unrest in 1989.